Concept used: In aqueous solution, the basic strength of amines depends on:

• the $+I$ effect of alkyl groups, which increases electron density on nitrogen and makes it more basic,
• solvation of the protonated amine in water, which stabilizes the conjugate acid.

Compare the given amines:

• Aniline ($\mathrm{C_6H_5NH_2}$): The lone pair on nitrogen is delocalized into the benzene ring by resonance, so it is much less available for protonation. Hence, aniline is the weakest base here.
• Methylamine ($\mathrm{CH_3NH_2}$): A primary aliphatic amine. The methyl group gives a $+I$ effect, increasing basicity compared to ammonia.
• Dimethylamine ($\mathrm{(CH_3)_2NH}$): A secondary amine. Two methyl groups increase electron density on nitrogen, and in aqueous solution its conjugate acid is still reasonably well solvated. This makes it very basic.
• Trimethylamine ($\mathrm{(CH_3)_3N}$): Though it has three methyl groups giving strong $+I$ effect, in aqueous solution the protonated form $\mathrm{(CH_3)_3NH^+}$ is less effectively solvated due to steric hindrance. So it is less basic than dimethylamine in water.

Order of basic strength in aqueous solution: $\mathrm{(CH_3)_2NH > CH_3NH_2 > (CH_3)_3N > C_6H_5NH_2}$

Therefore, the strongest base in aqueous solution is: $\boxed{\mathrm{Dimethylamine}}$

Option check:

• A: Trimethylamine — Incorrect
• B: Aniline — Incorrect
• C: Dimethylamine — Correct
• D: Methylamine — Incorrect